A spacecraft component layout optimization method considering rotational inertia and vibration frequency

Abstract

The present invention discloses a method for optimizing spacecraft component layout that considers moment of inertia and vibration frequency. The method includes presetting the dimensions of a spacecraft cabin and multiple components to be laid out and performing approximate descriptions thereof to obtain a three-dimensional approximate model. A Φ function is set based on the three-dimensional approximate model and non-interference constraints are calculated. A center of mass error constraint and a safety distance constraint are set. The spacecraft's moment of inertia is calculated. Finite element analysis is performed on the spacecraft structure, and a characteristic equation is set and solved to obtain the spacecraft's vibration frequency. A dual-objective optimization model for spacecraft component layout is constructed using the spacecraft's moment of inertia and vibration frequency as optimization objectives and the non-interference constraint, center of mass error constraint, and safety distance constraint as constraint terms. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain a spacecraft component layout optimization solution that satisfies the constraints. This method can efficiently and accurately handle spacecraft component layout optimization problems that simultaneously consider both mass characteristics and vibration frequency characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft design, and in particular to a spacecraft component layout optimization method considering rotational inertia and vibration frequency. Background Art

[0002] The key task of spacecraft design is to enable the spacecraft to carry high-precision instruments and equipment within certain constraints, such as mass and volume, and to maintain reliable long-term orbital operation. Spacecraft component layout design involves placing multiple components within a given, limited spacecraft space, while satisfying certain necessary constraints, to achieve optimal performance. Components performing different tasks must be spaced appropriately to ensure operational independence and efficiency, while components performing the same task must be properly arranged and placed to ensure consistent and accurate operation.

[0003] Currently, the design of spacecraft component layouts primarily relies on engineers' experience, resulting in a number of optimal layouts that meet the requirements of the spacecraft's mission. However, as the number of spacecraft components increases, and given the complex operating conditions of spacecraft in orbit, relying solely on experience to improve the effectiveness of layouts becomes increasingly difficult. Therefore, intelligent optimization of spacecraft component layouts can shorten spacecraft design cycles, reduce development costs, and improve overall spacecraft performance.

[0004] The layout problem is theoretically an NP-Hard problem. The spacecraft layout optimization problem belongs to a type of layout problem with performance constraints. The solution space of the optimization design problem considering the spacecraft performance objectives has the characteristics of strong constraints, high dimensions, multiple extreme values, non-convexity, and nonlinearity. It requires the comprehensive application of knowledge from various disciplines such as aerospace, statics, dynamics, geometry, and thermal science. Some scholars were the first to apply numerical optimization methods to the study of spacecraft component layout optimization design problems. They used a combination of sequential linear programming and feasible direction optimization methods to find the position of spacecraft payloads so that their inertial cross product is minimized, thereby reducing the need for spacecraft propulsion attitude control. At the same time, the geometric and electromagnetic interference between payloads are imposed as constraints. This combined strategy not only improves the efficiency and accuracy of the layout scheme, but also reduces the design cost and time. Some scholars considered the target performance of the spacecraft layout problem mainly in the overall mass distribution characteristics of the spacecraft, that is, the overall moment of inertia, the center of mass design position, etc. In addition to considering the target of the mass characteristic distribution of the spacecraft, some scholars also considered the thermal field distribution characteristics of the spacecraft, transformed the traditional single-objective spacecraft layout optimization problem into a multi-objective optimization problem, constructed two objective functions, namely the thermal dissipation function and the spacecraft center of mass function, and applied the research method to the layout design of the Brazilian multi-mission space platform. Some scholars further optimized the spacecraft layout design in theory based on the engineering practice of successful launches. The optimization process mainly considered optimization objectives such as mass characteristics, thermal uniformity, and residual magnetic strength.

[0005] Although research on spacecraft component layout has been ongoing for a long time, current research has primarily focused on designing optimization algorithms for single constraints. However, when multiple complex constraints are coupled, computational efficiency is low and computational costs increase exponentially. Furthermore, the use of a single optimization algorithm to solve such general problems is significantly limited. Furthermore, the multiphysics constraints considered are relatively simple and cannot fully describe the complex physical states of a spacecraft in orbit. Spacecraft layout optimization in multiphysics environments is a multi-objective, multi-constraint combinatorial optimization problem. Solving such problems is prone to optimization difficulties, low computational efficiency, and the tendency to fall into local optimal solutions. Consequently, research on spacecraft layout optimization based on high-fidelity multiphysics models has yet to be effectively carried out. Summary of the Invention

[0006] In order to solve the above problems, this application studies the model construction of the spacecraft component layout optimization design problem, mainly considering the two indicators of mass characteristics and dynamic characteristics, and proposes an effective spacecraft component layout optimization method.

[0007] A method for optimizing the layout of spacecraft components considering moment of inertia and vibration frequency, characterized in that the method comprises:

[0008] S1. Preset the dimensions of the spacecraft cabin and multiple components to be arranged, perform approximate descriptions of the spacecraft cabin and the multiple components to be arranged based on the dimensions, obtain three-dimensional approximate models of the spacecraft cabin and the multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system;

[0009] S2. Setting a Φ function between the three-dimensional approximate models corresponding to the components to be laid out and a Φ function between the three-dimensional approximate model of each component to be laid out and the three-dimensional approximate model of the spacecraft cabin according to the position parameters and calculating non-interference constraints;

[0010] S3. Preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid, and the actual centroid.

[0011] S4. Preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and establish a safety distance constraint between the components to be laid out based on the maximum safety distance threshold, the minimum safety distance threshold constraint, and the centroid distance between the components to be laid out;

[0012] S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft with respect to the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain the global stiffness matrix and the global mass matrix, set and solve the characteristic equation based on the global stiffness matrix and the global mass matrix, and obtain the vibration frequency of the spacecraft;

[0013] S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain a spacecraft component layout optimization solution that meets the constraints.

[0014] Preferably, the non-interference constraint in S2 is specifically expressed by the formula:

[0015]

[0016] Where c1(X) represents the total interference on the bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b, component 0 represents the spacecraft cabin, Δ 0b represents the interference between component b and the spacecraft cabin, and X represents the layout plan of the component to be laid out in the spacecraft cabin.

[0017] Preferably, the centroid error constraint in S3 is specifically expressed by the formula:

[0018] c2(X)=|x c -x e |-δx e ≤0

[0019] c3(X)=|y c -y e |-δy e ≤0

[0020] Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Represents the centroid error thresholds in the x and y directions, respectively, both are non-negative numbers.

[0021] Preferably, the safety distance constraint in S4 is specifically expressed by the formula:

[0022]

[0023] Where c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Indicates the centroid distance between components a and b to be laid out, and Respectively represent the minimum and maximum safety distance thresholds between components to be laid out.

[0024] Preferably, in S5, a finite element analysis is performed on the structure of the spacecraft to obtain a global stiffness matrix and a global mass matrix. A characteristic equation is set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows:

[0025] S51. Determine a plane four-node rectangular unit model corresponding to the bearing plate on the spacecraft cabin and perform finite element division to obtain a plurality of rectangular units;

[0026] S52. Randomly select a component to be laid out from the components to be laid out, calculate the distance between four nodes of each rectangular unit in a plurality of rectangular units and the selected component to be laid out, and use the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit;

[0027] S53, calculating the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the unit area constant stiffness matrix and mass matrix of the selected component to be laid out;

[0028] S54, selecting another component to be laid out from the components to be laid out until all components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out;

[0029] S55. A global stiffness matrix and a global mass matrix are obtained by assembling several rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

[0030] Preferably, the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected components to be laid out in S53 are specifically expressed by the formula:

[0031]

[0032] in,

[0033] Where, d j Indicates the distance from the jth node of each rectangular unit to the selected component to be laid out, H ε (d j ) is the Heaviside function value corresponding to the jth node of each rectangular unit, j = 1, 2, 3, 4, K c and M c K represents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out, e and M e represents the stiffness matrix and mass matrix of each rectangular element under the influence of the selected components to be laid out, ε represents the half bandwidth, and α represents a positive constant tending to zero.

[0034] Preferably, the dual-objective optimization model for spacecraft component layout in S6 is specifically expressed by the formula:

[0035]

[0036] Where X represents the layout scheme of the components to be arranged in the spacecraft cabin, f1(X) represents the moment of inertia of the spacecraft after the components to be arranged are arranged according to the layout scheme X, and f2(X) represents the vibration frequency of the spacecraft after the components to be arranged are arranged according to the layout scheme X.

[0037] Preferably, in S6, the dual-objective optimization model of the spacecraft component layout is optimized and solved to obtain an optimization solution for the spacecraft component layout that satisfies the constraint conditions. The specific process is as follows:

[0038] S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia;

[0039] S62. Derivation of the gradient of the eigenvalue based on the eigenvalue equation of the spacecraft, and conversion of the gradient of the calculated vibration frequency into the gradient of the calculated eigenvalue;

[0040] S63. Considering a diversity metric, the proposed layout schemes are expanded into a set of diversified layout schemes. Similarity is used to evaluate the diversity between any two layout schemes in the set of diversified layout schemes. The dual-objective optimization model for spacecraft component layout is transformed to obtain a spacecraft component layout optimization model that considers diversity and is optimized and solved to obtain several sets of diversified geometrically non-interference layout schemes.

[0041] S64. Using several groups of diverse geometric non-interference layout solutions as initial solutions and performing single-objective optimization on each of them, the optimal layout solution with the single objective performance is selected from the solutions with the best single objective performance.

[0042] S65. Based on the single-objective optimal layout solution, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with added orthogonal constraints. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with added orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout solutions in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization solutions that meet the constraints.

[0043] Preferably, the spacecraft component layout optimization model considering diversity in S63 is specifically expressed by the formula:

[0044]

[0045] Where, X * represents a variety of layout schemes, f(X * ) represents the objective function of the similarity of diverse layout schemes, similarity (m,n) Indicates the similarity between the mth layout scheme and the nth layout scheme in the diversified layout schemes, Indicates the position parameters of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. represents the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme, and M represents the total number of layout schemes after considering diversity.

[0046] Preferably, the single-objective optimization model with orthogonal constraints added in S65 is specifically expressed by the formula:

[0047]

[0048] Where, f * (X) represents the new Pareto approximation point to be solved, U l+1 and U l-1 They represent the two adjacent approximate points before and after the Pareto approximate point with the largest intelligent distance from the current known Pareto point, N 12 (*) indicates the vector corresponding to the constructed approximate line.

[0049] The above-mentioned spacecraft component layout optimization method considering moment of inertia and vibration frequency predefines the dimensions of the spacecraft cabin and multiple components to be laid out and approximates them separately to obtain a three-dimensional approximate model of the spacecraft cabin and the multiple components to be laid out. A reference coordinate system is constructed with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin. The position parameters of the three-dimensional approximate model corresponding to each component to be laid out in the reference coordinate system are predetermined. A Φ function is set and non-interference constraints are calculated. A center of mass error constraint and a safety distance constraint are set. A stellar coordinate system is constructed with the center of mass of the spacecraft as the coordinate origin. The moment of inertia of the spacecraft with respect to the stellar coordinate system is calculated. Finite element analysis is performed on the spacecraft structure. A characteristic equation is set and solved to obtain the vibration frequency of the spacecraft. A dual-objective optimization model for spacecraft component layout is constructed with the spacecraft's moment of inertia and vibration frequency as optimization objectives and the non-interference constraint, center of mass error constraint, and safety distance constraint as constraints. The dual-objective optimization model is optimized and solved to obtain a spacecraft component layout optimization solution that satisfies the constraints. This method can more efficiently and accurately handle spacecraft component layout optimization problems that simultaneously consider both mass characteristics and vibration frequency characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of a method for optimizing the layout of spacecraft components taking into account rotational inertia and vibration frequency in one embodiment of the present invention;

[0051] Figure 2 is a simplified schematic diagram of the overall structure of a spacecraft in one embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the layout of a single component to be arranged on a load-bearing plate in a spacecraft cabin in one embodiment of the present invention;

[0053] Figure 4 The effect of component layout on the stiffness matrix and mass matrix of a rectangular unit in one embodiment of the present invention;

[0054] Figure 5Schematic diagram of intelligent orthogonal constraint in one embodiment of the present invention;

[0055] Figure 6 is an area formed by a smart distance represented by a Lamé curve in one embodiment of the present invention;

[0056] Figure 7 This is a schematic diagram of the layout of six components to be arranged on a spacecraft bearing plate in one embodiment of the present invention;

[0057] Figure 8 This is a layout solution for minimizing the single objective of moment of inertia in one embodiment of the present invention;

[0058] Figure 9 This is a layout scheme for maximizing a single target of vibration frequency in one embodiment of the present invention;

[0059] Figure 10 Schematic diagram of an intelligent Pareto approximate optimal solution for dual-objective optimization of moment of inertia and vibration frequency in one embodiment of the present invention;

[0060] Figure 11 This is an example of a layout solution corresponding to some intelligent Pareto approximate optimal solutions in one embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0062] See also Figure 1 A spacecraft component layout optimization method considering rotational inertia and vibration frequency is provided, the method comprising the following steps:

[0063] S1. Preset the outer dimensions of the spacecraft cabin and multiple components to be arranged, make approximate descriptions of the spacecraft cabin and multiple components to be arranged based on their outer dimensions, obtain three-dimensional approximate models of the spacecraft cabin and multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset the position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system.

[0064] Specifically, referring to the structure of the classic multi-layer box-type spacecraft cabin, the mathematical model of the spacecraft engineering example is simplified. The simplified overall structure of the spacecraft is as follows: Figure 2 As shown in the figure, the spacecraft cabin is a rectangular parallelepiped, including side walls and load-bearing plates. To facilitate calculation, the load-bearing plates are designed as quadrilateral structures. The quadrilateral structure matches the cross-section of the spacecraft cabin in the xoy direction. The components to be laid out are approximately described as cylinders or rectangular parallelepipeds. The mass distribution of all components to be laid out is uniform, and the geometric centers coincide with the center of mass, as shown in the figure. Figure 3Consider the layout design of components on this bearing plate.

[0065] Describing the placement of aerospace components requires the introduction of three coordinate systems: a reference coordinate system, a celestial coordinate system, and a component coordinate system. The reference coordinate system, O-xyz, has its origin at the geometric center of the spacecraft's docking surface or installation measurement datum. This system is used to determine the placement and installation positions of each component to be placed and to calculate the coordinates of the spacecraft's center of mass. The celestial coordinate system, O'-x'y'z', has its origin at the spacecraft's center of mass and is used to determine the moment of inertia and product of inertia values ​​for the spacecraft's mass characteristics. The component coordinate system, O"-x"y"z", has its origin at the center of mass of each component to be placed and is used to calculate the moment of inertia of each component about its own coordinate axis.

[0066] In the reference coordinate system O-xyz, the position of each component to be laid out is represented by a set of position parameters (x i ,y i ,z i ,θ i ) means, where (x i ,y i ,z i ) represents the center coordinate of the component to be laid out, θ i Indicates the rotation angle of the component to be arranged around its center of mass. For the components to be arranged installed on the same bearing plate, since the installation base of these components to be arranged is the same, the coordinate z of all components to be arranged on the same bearing plate in the height direction is i It is known that the height of the component to be laid out determines the coordinate z of the component to be laid out in the height direction. i is half the height. In this way, the center of mass coordinates of the entire spacecraft in the height direction can be obtained through weighted calculation based on the component mass, and it remains unchanged during the optimization process. Therefore, the three-dimensional layout design problem is based on the two-dimensional layout design. Therefore, once the plane center coordinates and rotation angles of the components to be laid out are determined, the layout plan is determined. The layout plan for the components to be laid out in the spacecraft can be written as:

[0067] X={X i =(x i ,y i ,θ i )|i=1,2,...,N} (1)

[0068] Where, X i Indicates the position parameter of the i-th component to be laid out, N represents the number of components to be laid out, x i and y i Indicates the coordinate values ​​of the i-th component to be laid out along the x-direction and y-direction in the reference coordinate system, (x i ,y i) is determined by the geometric dimensions of the load-bearing plate corresponding to the i-th component to be arranged. For components to be arranged without placement angle requirements, θ i The value range is [0,π). For components to be laid out that require orthogonal placement, θ i The value of is {0,π / 2}. In particular, for components with a circular bottom surface, such as a cylinder, θ i Can be fixed to 0.

[0069] S2. Setting the Φ function between the three-dimensional approximate models corresponding to the components to be laid out and the Φ function between the three-dimensional approximate model of each component to be laid out and the three-dimensional approximate model of the spacecraft cabin according to the position parameters and calculating the non-interference constraints.

[0070] Specifically, when optimizing the layout of spacecraft components, the primary consideration is that no interference occurs between components or between components and the spacecraft cabin during installation. Taking a load-bearing plate in the spacecraft cabin as an example, the non-interference constraint on the load-bearing plate can be expressed as:

[0071]

[0072] Where c1(X) represents the total interference on the bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b. When a=0, component a represents the spacecraft cabin, Δ 0b Represents the interference between component b and the spacecraft cabin. The total interference is 0, which means there is no interference between components and between components and the spacecraft cabin.

[0073] During the spacecraft component layout design process, a three-dimensional approximate model is constructed based on the dimensions of the spacecraft cabin and multiple components to be laid out, and the position parameters are determined. The Φ function is calculated using the position parameters of the three-dimensional approximate model corresponding to the components, and the interference between the components is determined. The Φ function between the position parameters of the components should satisfy the following properties:

[0074]

[0075] Where a and b represent any two components to be laid out. Represents the distance between the three-dimensional approximate models corresponding to any two components a and b to be laid out. When , it means that the three-dimensional approximate models corresponding to the two components to be laid out do not interfere with each other. In this case, we can appropriately reduce Bring the two components to be laid out close to each other;

[0076] when When , it means that the boundaries of the 3D approximate models corresponding to the two components to be laid out are just touching;

[0077] when When , it means that the three-dimensional approximate models corresponding to the two components to be laid out have interfered with each other. In this case, you can increase the Separate the two components to be laid out from each other.

[0078] Therefore, by constructing the Φ function expression, the calculation of the interference between spacecraft components can be expressed by a completely equivalent Φ function value. The distance between the three-dimensional approximate models corresponding to the components a and b to be laid out can be calculated by the Φ function. like The interference amount Δ ab Set to 0, if This indicates that interference has occurred between the two components, and the specific amount of interference can be obtained.

[0079] S3. Preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid, and the actual centroid.

[0080] Specifically, the static stability of the spacecraft is also a factor that needs to be considered. If the static stability is too large, it will inevitably affect the maneuverability of the spacecraft. Therefore, when designing a spacecraft, the center of mass error between the actual center of mass of the spacecraft and the expected center of mass must be as small as possible and kept within an allowable error range. Generally, the geometric center of the spacecraft is taken as the expected center of mass. The center of mass error constraint can be described as:

[0081] c2(X)=|x c -x e |-δx e ≤0 (4)

[0082] c3(X)=|y c -y e |-δy e ≤0 (5)

[0083] Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Represents the centroid error thresholds in the x and y directions, respectively, both are non-negative numbers.

[0084] S4. Preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and construct a safety distance constraint between the components to be laid out based on the maximum safety distance threshold, the minimum safety distance threshold constraint, and the centroid distance between the components to be laid out.

[0085] Specifically, in the engineering practice of spacecraft design, it is found that some functional equipment may interact with each other during the on-orbit operation of the spacecraft, thereby affecting the working accuracy of the equipment. Considering the processing needs such as the installation of equipment components and wire layout in the spacecraft equipment compartment, a certain safety distance should be maintained when placing components. In addition, some or a group of collaborative equipment need to be kept within a feasible distance when working together. Once the threshold distance is exceeded, a subsystem of the spacecraft may not work properly. Therefore, this distance constraint is defined as a safety and feasibility constraint, which can be expressed as a minimum distance constraint or a maximum distance constraint:

[0086]

[0087] Where c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Indicates the centroid distance between components a and b to be laid out, which can be directly calculated. and They represent the minimum and maximum safe distance thresholds between components to be laid out, respectively, which are preset based on the spacecraft mission performance requirements. When considering the safe distance constraint, the case where a = 0 does not need to be considered.

[0088] S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft with respect to the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain the global stiffness matrix and the global mass matrix, set the characteristic equation based on the global stiffness matrix and the global mass matrix and solve it to obtain the vibration frequency of the spacecraft.

[0089] Specifically, the moment of inertia of a spacecraft reflects its inertia when rotating. To achieve more efficient attitude control, the spacecraft's moment of inertia is generally minimized during design. In the stellar coordinate system O'-x'y'z' used to calculate the moment of inertia, each axis of the stellar coordinate system is the central inertia axis of the spacecraft, so the moment of inertia of the spacecraft system is zero. The formula for calculating the moment of inertia of a spacecraft is:

[0090]

[0091] Where, I represents the moment of inertia of the spacecraft, I x′x′ , I y′y′ and I z′z′They are the moments of inertia of the spacecraft about the stellar coordinate system in the x', y' and z' axes, which can be directly calculated.

[0092] Furthermore, structural vibration is a key concern during spacecraft design. During the active phase of a spacecraft launch, it can experience resonance, which can cause structural damage or local instability, impacting the normal operation of the equipment and potentially leading to immeasurable consequences. Structural vibration is a relatively tangible, virtual problem, particularly in theoretical analysis of a structure's frequency, damping, and mode shapes. Vibration analysis typically involves establishing a concrete mathematical model and using software programming to visualize the data, simplifying the analytical and computational process.

[0093] Furthermore, in S5, a finite element analysis is performed on the structure of the spacecraft to obtain the global stiffness matrix and the global mass matrix. The characteristic equation is set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows:

[0094] S51. Determine a plane four-node rectangular unit model corresponding to the load-bearing plate on the spacecraft cabin and perform finite element division to obtain a plurality of rectangular units.

[0095] For the vibration analysis of the spacecraft component layout problem, in this embodiment, the area occupied by the bearing plate on the spacecraft cabin is represented by a plane four-node rectangular unit model and finite element division is performed to obtain a number of rectangular units. Figure 4 In the divided grid, the components to be laid out are regarded as uniform mass blocks, and the rectangular units occupied by the components to be laid out (corresponding to Figure 4 The non-blank grid in the represents the distribution of the stiffness and mass of the components to be laid out. Therefore, changes in the position of the components to be laid out will lead to changes in the structural stiffness and mass matrices of the rectangular elements, further affecting the global stiffness and mass matrices of the spacecraft structure.

[0096] S52 , randomly selecting a component to be laid out from the components to be laid out, calculating the distances between four nodes of each of the plurality of rectangular units and the selected component to be laid out, and using the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit.

[0097] First, calculate the distance between the four nodes of each rectangular unit in several rectangular units and the selected components to be laid out, and judge the influence of the selected layout components on the stiffness matrix and mass matrix of each rectangular unit based on the distance: if the node is far away from the component to be laid out, it means that the stiffness matrix and mass matrix of the rectangular unit corresponding to the node are not affected by the component to be laid out, such as Figure 4Most of the black nodes in the grid; if the node is very close to the component to be laid out or the node is inside the component to be laid out, it means that the stiffness matrix and mass matrix of the rectangular unit corresponding to the node are affected by the component to be laid out, such as Figure 4 The bold black nodes. At the boundary of the component to be laid out (corresponding to Figure 4 The degree to which the nodes near the black solid line in the figure are affected by the components to be laid out is approximately described using the Heaviside function:

[0098]

[0099] Where H ε (d j ) represents the Heaviside function value corresponding to the jth node of each rectangular unit, that is, the degree to which the jth node is affected by the selected component to be laid out, d j The distance between the jth node of each rectangular unit and the selected component to be laid out can be directly calculated, j = 1, 2, 3, 4. If the calculated distance is a negative value, it means that the jth node of the rectangular unit is inside the selected component to be laid out. If the calculated distance is a positive value, it means that the jth node of the rectangular unit is outside the selected component to be laid out. ε represents the half-bandwidth, which is generally 1-2 unit cells in size. α represents a small amount to avoid the occurrence of matrix singularity.

[0100] S53. Calculate the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the stiffness matrix and mass matrix of the selected component to be laid out.

[0101] The stiffness matrix and mass matrix of each rectangular element in the planar four-node rectangular element model under the influence of the selected layout components can be expressed by the Heaviside function values ​​corresponding to the four nodes:

[0102]

[0103] Where K e and M e represents the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected layout components, d j Represents the distance from the jth node of each rectangular unit to the selected component to be laid out, j = 1, 2, 3, 4, H ε (d j ) is d j The corresponding Heaviside function value, K c and M cRepresents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out. If a rectangular unit is completely covered by a component to be laid out, then the four nodes of the rectangular unit are all inside the component to be laid out, and the corresponding Heaviside function values ​​are all 1. Then the stiffness matrix and mass matrix of the rectangular unit are the unit area constant stiffness matrix and mass matrix of the component, respectively, that is: K e =K c , M e =M c .

[0104] Furthermore, when the stiffness matrix and mass matrix of each rectangular unit are calculated by the above calculation method, the calculation of the mass matrix and stiffness matrix corresponding to the rectangular units that intersect with the boundaries of the selected components to be laid out is obviously inaccurate. The multi-resolution finite element method can be used to further subdivide the rectangular units that intersect with the boundaries of the selected components to be laid out, such as Figure 4 As shown in the partial enlarged view of , the rectangular elements that intersect with the boundaries of the selected rectangular component to be laid out are further divided inside it, and the above calculation process is repeated to more accurately determine the mass matrix and stiffness matrix of the rectangular elements.

[0105] The load-bearing plate of the spacecraft cabin itself also needs to consider the stiffness matrix and mass matrix. Therefore, the stiffness matrix and mass matrix obtained by the influence of the above-mentioned components to be laid out on the rectangular unit should be further superimposed on the basis of the load-bearing plate itself.

[0106] S54, selecting another component to be laid out from the components to be laid out until all components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out;

[0107] S55. A global stiffness matrix and a global mass matrix are obtained by assembling several rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

[0108] Specifically, using standard finite element analysis procedures, the global stiffness matrix K and global mass matrix M are obtained by assembling rectangular elements. K and M vary with the component layout. Derivation of the global stiffness matrix and global mass matrix based on the mass and stiffness matrices of each rectangular element is a well-established fundamental theory of the finite element method and will not be further elaborated here.

[0109] The analysis of the inherent characteristics of spacecraft structures during vibration can be reduced to solving the following discrete form of the eigenvalue equation:

[0110] Kφ=λMφ (12)

[0111] Where λ = ω 2 ,φ T Mφ=1

[0112] Where K and M are the global stiffness matrix and global mass matrix of the spacecraft structure, respectively, ω is the vibration frequency, λ is the eigenvalue, and φ is the eigenmode.

[0113] Therefore, rewriting the above discrete form of the eigenvalue equation, we get the characteristic equation |K-ω 2 When M|=0 and the solution is obtained, the vibration frequency ω obtained is also variable.

[0114] S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain a spacecraft component layout optimization solution that meets the constraints.

[0115] Furthermore, the dual-objective optimization model for spacecraft component layout is as follows:

[0116]

[0117] Where ω represents the vibration frequency of the spacecraft.

[0118] When considering the dynamic objectives, maximizing the vibration frequency of the spacecraft is selected as the design objective to suppress resonance. Since optimization problems are generally handled by minimizing the objective function, the opposite of the vibration frequency is used as the optimization objective here. When considering the non-interference constraints between components, since equality constraints will strictly limit the values ​​of the design variables and reduce the degrees of freedom of design, the equality constraints are rewritten as inequality constraints, thus constituting a dual-objective optimization problem.

[0119] Theoretically, a spacecraft's moment of inertia is minimized when all components are close together. However, the close proximity of components and their distance from the fixed support boundaries in this situation leads to localized stiffness and mass concentration within the spacecraft, resulting in a low vibration frequency. However, to maximize the vibration frequency, components must be placed close to the fixed support boundaries, which increases the moment of inertia. These two objectives conflict, so the optimal solution to the layout design problem, which simultaneously optimizes both the moment of inertia and the vibration frequency, should be a set of Pareto-optimal solutions.

[0120] In order to optimize and solve the dual-objective optimization model of spacecraft component layout (corresponding to formula (13)), the present invention proposes a gradient-based and diverse multi-objective optimization algorithm, and solves the problem by deriving the analytical / semi-analytical sensitivity (i.e., gradient) of the objectives (including moment of inertia and vibration frequency) during gradient calculation.

[0121] Furthermore, in S6, the dual-objective optimization model of spacecraft component layout is optimized and solved to obtain the spacecraft component layout optimization solution that meets the constraints. The specific process is as follows:

[0122] S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia.

[0123] S62. The gradient of the eigenvalue is derived based on the eigenvalue equation of the spacecraft, and the gradient of the calculated vibration frequency is converted into the gradient of the calculated eigenvalue.

[0124] Specifically, the calculation of the moment of inertia can be obtained by an analytical formula (Formula (8)) according to the definition, and its corresponding gradient calculation is also easy to obtain. However, the calculation process of the vibration frequency is relatively complicated: if its gradient is directly derived, it involves changes in the stiffness matrix and the mass matrix, and the calculation process is relatively cumbersome; if the difference method is directly used to approximate the gradient calculation, it will bring certain numerical errors. Therefore, a semi-analytical sensitivity method is used to solve the gradient of the vibration frequency. The process is as follows:

[0125] If the eigenvalue λ is a single eigenvalue (i.e., its corresponding eigenmode φ is unique), then λ is differentiable, and the eigenvalue equation (corresponding to formula (12)) for the design variable (i.e., location parameter) x i Derivation gives:

[0126]

[0127] Multiply both ends of the above formula by φ T , using the symmetry of the stiffness matrix and mass matrix and the eigenvalue equation to simplify, we get the calculation formula of the gradient of the single eigenvalue to the design variable, which is specifically expressed as follows:

[0128]

[0129] Here, λ and φ are solved in advance by the eigenvalue equation.

[0130] The above formula (15) can be used to solve problems involving eigenfrequency optimization or constraints. and The sensitivity is calculated using the differential method, which is called semi-analytical sensitivity.

[0131] According to λ=ω 2It is easy to see that the changing trends of the eigenfrequency ω and the eigenvalue λ are the same. Therefore, in the design example, the gradient of the eigenvalue λ can be directly calculated instead of the gradient of the eigenfrequency ω.

[0132] S63. Considering the diversity measurement index, the layout scheme to be arranged is expanded into a set of diversified layout schemes. The diversity between any two layout schemes in a set of diversified layout schemes is evaluated using cosine similarity. The dual-objective optimization model of spacecraft component layout is transformed to obtain the spacecraft component layout optimization model considering diversity and optimize the solution to obtain several sets of diversified geometric non-interference layout schemes.

[0133] Specifically, since gradient optimization has a serious dependence on initial values, it is very easy to fall into the local optimum after iteration, so it is difficult to obtain a layout solution with the best global performance. In order to obtain more and better layout solutions, it is not possible to simply optimize by randomly generating many initial layout solutions. This method is not only time-consuming and labor-intensive, but also unscientific. Therefore, the idea of ​​diversity metrics can be added to the optimization process to guide the optimization to produce layout solutions with diversity. The spacecraft component layout optimization problem considers a variety of performance indicators and calculates the degree of diversity of a set of layout solutions. Therefore, in addition to the design objectives being different from those of traditional optimization problems, the design variables are also different from those of traditional optimization problems. The layout solutions of the components to be laid out are expanded into a set of diversified layout solutions, which can be expressed as:

[0134]

[0135] Where, X * Indicates a variety of layout options, It represents the position parameter of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. M represents the total number of layout schemes after considering diversity in each optimization process. Indicates the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes.

[0136] In the spacecraft component layout optimization problem, each layout solution in a set of layout solutions uniquely corresponds to a set of vectors describing the geometric position coordinates. Therefore, the diversity metric chosen is vector-based. The cosine similarity can be used to evaluate the diversity between two layout solutions:

[0137]

[0138] Where, X m Represents the vector corresponding to the mth layout scheme in the diversified layout scheme, X n Represents the vector corresponding to the nth layout scheme in the diversified layout scheme, similarity (m,n)Represents the similarity between the mth layout scheme and the nth layout scheme, 1≤m,n≤M.

[0139] Or use Gaussian similarity to calculate the distance between the vectors corresponding to two layout solutions to evaluate the diversity between the two solutions:

[0140]

[0141] Wherein, σ represents the bandwidth function determined by the vectors corresponding to the mth layout scheme and the nth layout scheme in the diversified layout schemes.

[0142] Therefore, the spacecraft component layout optimization model considering diversity is specifically expressed as:

[0143]

[0144] Where, f(X * ) represents the objective function of the similarity of diverse layout schemes, X * Indicates diverse layout solutions, similarity (m,n) Represents the similarity between the mth and nth layout schemes in the diverse layout schemes. The similarity value represents the similarity between two diverse layout schemes, so obtaining the layout scheme with the greatest diversity is equivalent to obtaining the layout scheme with the smallest similarity. In addition, in this optimization problem, the objective function is to limit the similarity between the overall schemes by controlling the maximum value of the similarity between the diverse layout schemes. After traversing all the layout schemes, the similarity between any two layout schemes should be obtained. There will be multiple similarity values. Here, only the maximum value of the similarity is limited, and the lower the maximum value of the similarity is, the better. The lower the maximum value of the similarity is, the higher the diversity of the layout schemes will be.

[0145] The above-mentioned spacecraft component layout optimization model considering diversity (corresponding to formula (18)) is optimized and solved to obtain several sets of diverse geometric non-interference layout schemes.

[0146] S64. Take several groups of diverse geometric non-interference layout solutions as initial solutions and perform single-objective optimization on them respectively, and select the best single-objective layout solution from the solutions with better single-objective performance.

[0147] S65. Based on the single-objective optimal layout solution, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with added orthogonal constraints. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with added orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout solutions in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization solutions that meet the constraints.

[0148] Specifically, in order to solve the spacecraft component layout optimization problem considering multi-physics field performance (such as the moment of inertia I and vibration frequency ω in this application), the Pareto front generation mechanism SNC (Smart Normal Constraint) is first introduced into the layout optimization algorithm. The main idea of ​​SNC is to transform the multi-objective optimization problem into several single-objective optimization problems by continuously adding and updating linear constraints during the optimization process, limiting the scope of the solution space, and then solving it in a specific design space, such as Figure 5 shown.

[0149] Furthermore, the specific process of S65 is as follows:

[0150] S651. Use the two single-objective optimal layout solutions as reference positioning points, and connect the two reference positioning points to construct an approximate line.

[0151] Figure 5 In, f 1* The layout scheme corresponding to the target value f1 of the moment of inertia and the maximum target value f2 of the vibration frequency is the smallest, f 2* The layout plan corresponding to the minimum moment of inertia target value f1 and the maximum vibration frequency target value f2 is to connect these two points f 1* and f 2* Construct an approximate line.

[0152] S652: Preset a smart distance threshold, generate a number of evenly distributed approximate points on the approximate line, calculate the smart distance between two adjacent approximate points, compare the smart distance with the smart distance threshold, and screen out multiple approximate points that meet the smart distance threshold requirement.

[0153] The calculation formula for the i-th approximate point is:

[0154]

[0155] in,

[0156] Where, and It is a parameter variable, and the increment δ can be fixed from 0 to 1, so that uniformly distributed points are generated on the Pareto frontier. δ is given according to actual needs. A smaller δ value will produce a larger number of approximate points. Generally, represents the minimum Euclidean distance from a point to its surrounding PIT (Practically Insignificant Trade-off) region that defines a smart distance, d represents the distance vector between the center points of two PIT regions, P 1 and P 2These are the constructed approximate Pareto frontier vertices, corresponding to the reference positioning points corresponding to the two single-objective optimal layout solutions in S651.

[0157] In the SNC algorithm, the generation of the Pareto solution set is determined by the smart distance between the approximate points in the design space. The definition of smart distance is that no approximate point in the Pareto solution set falls within the region formed by the smart distance corresponding to any other approximate point. The region formed by the smart distance can be represented by a Lamé curve, see Figure 6 , Figure 6 The area enclosed by the four arc segments is the area formed by the smart distance corresponding to a certain approximate point. The calculation formula of the smart distance s is as follows:

[0158] s=||Ad|| p ,0≤p≤2 (20)

[0159] in,

[0160] Where s represents the smart distance, A is a user-defined vector, d is the distance metric between the center points of two PIT regions (i.e., approximate points), and ||Ad|| p is the p-norm of vector Ad, a i (i=1,2) and p are user-defined parameters used to determine the distribution of the intelligent Pareto points for a specific problem. i (i=1,2) corresponds to the change in the i-th design goal that can cause a significant difference between two approximate points when other design goals remain unchanged. The threshold of the preset smart distance s is 1. The smart distance s between any two adjacent approximate points must be greater than 1 to meet the requirement. Through screening, multiple approximate points that meet the requirements are obtained.

[0161] S653. Take multiple approximate points as known Parato points, add orthogonal constraints to the dual-objective optimization model of spacecraft component layout, and use the gradient algorithm to solve the single-objective optimization model with orthogonal constraints through the gradient of the moment of inertia and the gradient of the eigenvalue. Generate new Parato points and determine whether to retain them. The retained new Parato points constitute the intelligent Pareto approximate optimal solution set.

[0162] Furthermore, the single-objective optimization model with orthogonal constraints is described as:

[0163]

[0164] Where, f * (X) represents the new Pareto point to be solved, U l is the Pareto approximate point with the largest intelligent distance from the currently known Pareto point, Ul+1 and U l-1 They represent the Pareto approximate point U with the largest intelligent distance from the current known Pareto point. l The two adjacent approximate points before and after, N 12 (*) indicates the connection point f 1* and f 2* Construct the vector corresponding to the approximate line, where f 1* The layout scheme corresponding to the target value f1 of the moment of inertia and the maximum target value f2 of the vibration frequency is the smallest, f 2* Layout plan corresponding to the minimum moment of inertia target value f1 and the maximum vibration frequency target value f2.

[0165] like Figure 5 As shown, the additional linear constraints here correspond to Figure 5 The shaded area in the figure is perpendicular to the approximation line and is therefore called an orthogonal constraint. By solving the problem using a gradient algorithm based on the gradient of the moment of inertia and the gradient of the vibration frequency, a new Pareto point can be generated. However, the new Pareto point generated by single-objective optimization does not necessarily fall within the intelligent Pareto optimal solution set. Therefore, it is necessary to determine whether to retain the new Pareto point based on the dominant solution and the intelligent distance. The retained new Pareto points constitute the intelligent Pareto approximate optimal solution set.

[0166] The unique feature of this smart distance method is that it requires only a single scalar value, the smart distance, to define the region of smart distances corresponding to the approximate points. This allows the algorithm to identify whether a new Pareto point is a smart Pareto approximate optimal solution and to determine the extent to which this point is smart. As a result, the SNC method can more efficiently search the design space and determine which known Pareto points are most likely to generate new Pareto points.

[0167] Furthermore, a spacecraft component layout optimization method considering the moment of inertia and vibration frequency in the present invention is verified through numerical simulation.

[0168] like Figure 7 As shown, Figure 7 As shown in the figure, within a 10×10 2D rectangular design area D on the bearing plate surface, three cubic components measuring 4×4×4 and three cylindrical components with a base radius of 2 and a height of 4 are required, with a mass of 10 for each component. The desired deviation between the center of mass of the structure and the geometric center of the spacecraft is no more than 0.001, and the minimum safe distance threshold between components is 0.2. Furthermore, the bearing plate is designed to be mounted with four-side clamped support as the boundary condition.

[0169] Firstly, a diversified initial value single-objective gradient optimization algorithm is used to solve the layout solutions for minimizing the moment of inertia and maximizing the vibration frequency respectively.

[0170] Then, the optimal layout scheme with a single objective is selected from several groups of diverse layout schemes obtained by solution.

[0171] See also Figure 8 and Figure 9 , Figure 8 The following shows the layout scheme with the minimum moment of inertia. At this time, the target moment of inertia is 2203.74, and the corresponding vibration frequency characteristic value of this layout scheme is 24305.25. Figure 9 The figure shows the layout scheme for the maximum vibration frequency eigenvalue, which is 39019.95, and the corresponding moment of inertia for this layout scheme is 8952.72. It is not difficult to see that, driven by the moment of inertia optimization objective, the components to be laid out converge toward the center. However, driven by the maximum vibration frequency objective, the components to be laid out disperse toward the boundaries, achieving a local optimum in target performance. These two layout results show that both single-objective optimal layout schemes effectively prevent interference between components. Furthermore, using a gradient optimization method based on semi-analytical sensitivity techniques, it is possible to identify a layout optimization scheme with superior performance for a specific physical field of the spacecraft system.

[0172] Then, the intelligent orthogonal constraint method is introduced, and the single-objective optimal layout solution obtained above is used as the reference positioning point for multi-objective optimization for further optimization, and the intelligent Pareto approximate optimal solution set is obtained.

[0173] like Figure 10 As shown, Figure 10 The paper presents a set of intelligent Pareto-like approximate optimal solutions for a dual-objective optimization scenario with moment of inertia and vibration frequency as the targets. In addition to the two layout solutions used as reference points for the single-objective optimization, 15 additional layout solutions were obtained. These 15 layout solutions balance the optimization objectives of moment of inertia and vibration frequency. The corresponding target values ​​for each layout solution are shown in Table 1.

[0174]

[0175]

[0176] Figure 11 The following diagram shows the layout scheme corresponding to some intelligent Pareto approximate optimal solution sets, where Figure 11 (a) Schematic diagram of the layout corresponding to Scheme 5 in Table 1; Figure 11 (b) Schematic diagram of the layout corresponding to Scheme 6 in Table 1; Figure 11 (c) Schematic diagram of the layout corresponding to Scheme 12 in Table 1.

[0177] It can be seen from the above numerical simulation verification that the diversified initial value single-objective gradient optimization algorithm combined with the intelligent orthogonal constraint method can better solve the dual-objective optimization problem of spacecraft component layout.

[0178] The above-mentioned spacecraft component layout optimization method considering the moment of inertia and vibration frequency presets the outer dimensions of the spacecraft cabin and multiple components to be laid out and makes approximate descriptions thereof, obtains a three-dimensional approximate model of the spacecraft cabin and multiple components to be laid out, constructs a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, presets the position parameters of the three-dimensional approximate model corresponding to each component to be laid out in the reference coordinate system, sets the Φ function and calculates the non-interference constraint, sets the center of mass error constraint and the safety distance constraint, constructs a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculates the moment of inertia of the spacecraft with respect to the stellar coordinate system, performs finite element analysis on the structure of the spacecraft, sets the characteristic equation and solves it, obtains the vibration frequency of the spacecraft, takes the moment of inertia and vibration frequency of the spacecraft as optimization targets, constructs a dual-objective optimization model for spacecraft component layout with the non-interference constraint, the center of mass error constraint and the safety distance constraint as constraint items, optimizes and solves the dual-objective optimization model for spacecraft component layout, and obtains a spacecraft component layout optimization scheme that meets the constraint conditions. This method uses the φ function to characterize the geometric and positional relationships between components, more efficiently handling the non-interference constraints between components. When calculating the vibration frequency of the spacecraft instrument panel, the finite element method is used to construct the stiffness and mass of the structure, improving the accuracy of the calculation. In addition, for the spacecraft component layout optimization problem that simultaneously considers the mass characteristics and vibration frequency characteristics, a gradient-based diversified multi-objective optimization algorithm is designed, and the derivation of semi-analytical sensitivity is given, which greatly saves the tedious gradient calculation work.

[0179] The above describes in detail the spacecraft component layout optimization method provided by the present invention that takes into account the moment of inertia and vibration frequency. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only intended to help understand the core concept of the present invention. It should be noted that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the layout of spacecraft components considering moment of inertia and vibration frequency, characterized in that: The method comprises: S1. Preset the dimensions of the spacecraft cabin and multiple components to be arranged, perform approximate descriptions of the spacecraft cabin and the multiple components to be arranged based on the dimensions, obtain three-dimensional approximate models of the spacecraft cabin and the multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system; S2. Setting a Φ function between the three-dimensional approximate models corresponding to the components to be laid out and a Φ function between the three-dimensional approximate model of each component to be laid out and the three-dimensional approximate model of the spacecraft cabin according to the position parameters and calculating non-interference constraints; S3. Preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid, and the actual centroid. S4. Preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and establish a safety distance constraint between the components to be laid out based on the maximum safety distance threshold, the minimum safety distance threshold, and the centroid distance between the components to be laid out; S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft with respect to the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain the global stiffness matrix and the global mass matrix, set and solve the characteristic equation based on the global stiffness matrix and the global mass matrix, and obtain the vibration frequency of the spacecraft; S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain a spacecraft component layout optimization solution that meets the constraints.

2. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 1, characterized in that: The non-interference constraint in S2 is specifically expressed as follows: Where c1(X) represents the total interference on the bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b, component 0 represents the spacecraft cabin, Δ 0b represents the interference between component b and the spacecraft cabin, and X represents the layout plan of the component to be laid out in the spacecraft cabin.

3. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 2, characterized in that: The centroid error constraint in S3 is specifically expressed as follows: c2(X)=|x c -x e |-δx e ≤0 c3(X)=|y c -y e |-δy e ≤0 Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Represents the centroid error thresholds in the x and y directions, respectively, both are non-negative numbers.

4. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 3, characterized in that: The safety distance constraint in S4 is specifically expressed as follows: Where c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Indicates the centroid distance between components a and b to be laid out, and Respectively represent the minimum and maximum safety distance thresholds between components to be laid out.

5. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 4, characterized in that: In S5, finite element analysis is performed on the structure of the spacecraft to obtain the global stiffness matrix and global mass matrix. The characteristic equation is set and solved according to the global stiffness matrix and global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows: S51. Determine a plane four-node rectangular unit model corresponding to the bearing plate on the spacecraft cabin and perform finite element division to obtain a plurality of rectangular units; S52. Randomly select a component to be laid out from the components to be laid out, calculate the distance between four nodes of each rectangular unit in a plurality of rectangular units and the selected component to be laid out, and use the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit; S53, calculating the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the unit area constant stiffness matrix and mass matrix of the selected component to be laid out; S54, selecting another component to be laid out from the components to be laid out until all components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out; S55. A global stiffness matrix and a global mass matrix are obtained by assembling several rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

6. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 5, characterized in that: The stiffness matrix and mass matrix of each rectangular element in S53 under the influence of the selected components to be laid out are specifically expressed as follows: in, Where, d j Indicates the distance from the jth node of each rectangular unit to the selected component to be laid out, H ε (d j ) is the Heaviside function value corresponding to the jth node of each rectangular unit, j = 1, 2, 3, 4, K c and M c K represents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out, e and M e represents the stiffness matrix and mass matrix of each rectangular element under the influence of the selected components to be laid out, ε represents the half bandwidth, and α represents a positive constant tending to zero.

7. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 6, characterized in that: The dual-objective optimization model for spacecraft component layout in S6 is specifically expressed as follows: Where X represents the layout scheme of the components to be arranged in the spacecraft cabin, f1(X) represents the moment of inertia of the spacecraft after the components to be arranged are arranged according to the layout scheme X, and f2(X) represents the vibration frequency of the spacecraft after the components to be arranged are arranged according to the layout scheme X.

8. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 7, characterized in that: In S6, the dual-objective optimization model of spacecraft component layout is optimized and solved to obtain the spacecraft component layout optimization solution that meets the constraints. The specific process is as follows: S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia; S62. Derivation of the gradient of the eigenvalue based on the eigenvalue equation of the spacecraft, and conversion of the gradient of the calculated vibration frequency into the gradient of the calculated eigenvalue; S63. Considering a diversity metric, the proposed layout schemes are expanded into a set of diversified layout schemes. Similarity is used to evaluate the diversity between any two layout schemes in the set of diversified layout schemes. The dual-objective optimization model for spacecraft component layout is transformed to obtain a spacecraft component layout optimization model that considers diversity and is optimized and solved to obtain several sets of diversified geometrically non-interference layout schemes. S64. Using several groups of diverse geometric non-interference layout solutions as initial solutions and performing single-objective optimization on each of them, the optimal layout solution with the single objective performance is selected from the solutions with the best single objective performance. S65. Based on the single-objective optimal layout solution, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with added orthogonal constraints. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with added orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout solutions in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization solutions that meet the constraints.

9. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 8, characterized in that: The spacecraft component layout optimization model considering diversity in S63 is specifically expressed by the formula: Where, X * represents a variety of layout schemes, f(X * ) represents the objective function of the similarity of diverse layout schemes, similarity (m,n) Indicates the similarity between the mth layout scheme and the nth layout scheme in the diversified layout schemes, Indicates the position parameters of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. represents the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme, and M represents the total number of layout schemes after considering diversity.

10. The spacecraft component layout optimization method considering rotational inertia and vibration frequency according to claim 9, characterized in that: The single-objective optimization model with orthogonal constraints added in S65 is specifically expressed as follows: Where, f * (X) represents the new Pareto approximation point to be solved, U l+1 and U l-1 They represent the two adjacent approximate points before and after the Pareto approximate point with the largest intelligent distance from the current known Pareto point, N 12 (*) indicates the vector corresponding to the constructed approximate line.

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